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1
Content available remote

Copula-based dependence measures

100%
Liebscher E.
Dependence Modeling
|
2014
|
tom 2
|
nr 1
EN
The aim of the present paper is to examine two wide classes of dependence coefficients including several well-known coefficients, for example Spearman’s ρ, Spearman’s footrule, and the Gini coefficient. There is a close relationship between the two classes: The second class is obtained by a symmetrisation of the coefficients in the former class. The coefficients of the first class describe the deviation from monotonically increasing dependence. The construction of the coefficients can be explained by geometric arguments. We introduce estimators of the dependence coefficients and prove their asymptotic normality.
2
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Copula-Based Dependence Measures For Piecewise Monotonicity

100%
Liebscher E.
Dependence Modeling
|
2017
|
tom 5
|
nr 1
198-220
EN
The aim of the present paper is to develop and examine association coefficients which can be helpfully applied in the framework of regression analysis. The construction of the coeffiecients is connected with the well-known Spearman coeffiecient and extensions of it (see Liebscher [5]). The proposed coeffiecient measures the discrepancy between the data points and a function which is strictly increasing on one interval and strictly decreasing in the remaining domain.We prove statements about the asymptotic behaviour of the estimated coeffiecient (convergence rate, asymptotic normality).
3
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Dependence of Stock Returns in Bull and Bear Markets

81%
Dobric J., Frahm G., Schmid F.
Dependence Modeling
|
2013
|
tom 1
94-110
EN
Despite of its many shortcomings, Pearson’s rho is often used as an association measure for stock returns. A conditional version of Spearman’s rho is suggested as an alternative measure of association. This approach is purely nonparametric and avoids any kind of model misspecification. We derive hypothesis tests for the conditional rank-correlation coefficients particularly arising in bull and bear markets and study their finite-sample performance by Monte Carlo simulation. Further, the daily returns on stocks contained in the German stock index DAX 30 are analyzed. The empirical study reveals significant differences in the dependence of stock returns in bull and bear markets.
4
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A note on the Galambos copula and its associated Bernstein function

81%
Mai J.-F.
Dependence Modeling
|
2014
|
tom 2
|
nr 1
EN
There is an infinite exchangeable sequence of random variables {Xk}k∈ℕ such that each finitedimensional distribution follows a min-stable multivariate exponential law with Galambos survival copula, named after [7]. A recent result of [15] implies the existence of a unique Bernstein function Ψ associated with {Xk}k∈ℕ via the relation Ψ(d) = exponential rate of the minimum of d members of {Xk}k∈ℕ. The present note provides the Lévy–Khinchin representation for this Bernstein function and explores some of its properties.
5
Content available remote

Dependence Measuring from Conditional Variances

81%
Kamnitui N., Santiwipanont T., Sumetkijakan S.
Dependence Modeling
|
2015
|
tom 3
|
nr 1
EN
A conditional variance is an indicator of the level of independence between two random variables. We exploit this intuitive relationship and define a measure v which is almost a measure of mutual complete dependence. Unsurprisingly, the measure attains its minimum value for many pairs of non-independent ran- dom variables. Adjusting the measure so as to make it invariant under all Borel measurable injective trans- formations, we obtain a copula-based measure of dependence v* satisfying A. Rényi’s postulates. Finally, we observe that every nontrivial convex combination of v and v* is a measure of mutual complete dependence.
6
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Measuring association via lack of co-monotonicity: the LOC index and a problem of educational assessment

81%
Qoyyimi D. T., Zitikis R.
Dependence Modeling
|
2015
|
tom 3
|
nr 1
EN
Measuring association, or the lack of it, between variables plays an important role in a variety of research areas, including education,which is of our primary interest in this paper. Given, for example, student marks on several study subjects, we may for a number of reasons be interested in measuring the lack of comonotonicity (LOC) between the marks, which rarely follow monotone, let alone linear, patterns. For this purpose, in this paperwe explore a novel approach based on a LOCindex,which is related to, yet substantially different from, Eckhard Liebscher’s recently suggested coefficient of monotonically increasing dependence. To illustrate the new technique,we analyze a data-set of student marks on mathematics, reading and spelling.
7
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Inference for copula modeling of discrete data: a cautionary tale and some facts

62%
Faugeras O. P.
Dependence Modeling
|
2017
|
tom 5
|
nr 1
121-132
EN
In this note, we elucidate some of the mathematical, statistical and epistemological issues involved in using copulas to model discrete data. We contrast the possible use of (nonparametric) copula methods versus the problematic use of parametric copula models. For the latter, we stress, among other issues, the possibility of obtaining impossible models, arising from model misspecification or unidentifiability of the copula parameter.
8
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Bivariate copulas, norms and non-exchangeability

62%
Papini P. L.
Dependence Modeling
|
2015
|
tom 3
|
nr 1
EN
The present paper is related to the study of asymmetry for copulas by introducing functionals based on different norms for continuous variables. In particular, we discuss some facts concerning asymmetry and we point out some flaws occurring in the recent literature dealing with this matter.
9
Content available remote

Generalized covariance inequalities

52%
Matuła P., Ziemba M.
Open Mathematics
|
2011
|
tom 9
|
nr 2
281-293
EN
We prove some inequalities for the difference between a joint distribution and the product of its marginals for arbitrary absolutely continuous random variables. Some applications of the obtained inequalities are also presented.
10
Content available remote

New copulas based on general partitions-of-unity and their applications to risk management (part II)

52%
Pfeifer D., Mändle A., Ragulina O.
Dependence Modeling
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2017
|
tom 5
|
nr 1
246-255
EN
We present a constructive and self-contained approach to data driven infinite partition-of-unity copulas that were recently introduced in the literature. In particular, we consider negative binomial and Poisson copulas and present a solution to the problem of fitting such copulas to highly asymmetric data in arbitrary dimensions.
11
Content available remote

Dependent defaults and losses with factor copula models

42%
Ackerer D., Vatter T.
Dependence Modeling
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2017
|
tom 5
|
nr 1
375-399
EN
We present a class of flexible and tractable static factor models for the term structure of joint default probabilities, the factor copula models. These high-dimensional models remain parsimonious with paircopula constructions, and nest many standard models as special cases. The loss distribution of a portfolio of contingent claims can be exactly and efficiently computed when individual losses are discretely supported on a finite grid. Numerical examples study the key features affecting the loss distribution and multi-name credit derivatives prices. An empirical exercise illustrates the flexibility of our approach by fitting credit index tranche prices.
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